Adaptive dynamic surface control with Nussbaum gain for course-keeping of ships

Combining dynamic surface control and Nussbaum gain function with backstepping algorithm, a novel adaptive nonlinear control strategy is proposed for the nonlinear course control problem of ships with parameter uncertainties and completely unknown control coefficient. Dynamic surface control is incorporated into backstepping technique to overcome the problem of its inherent “explosion of terms” so that the control law is simpler and easier to implement in engineering. Nussbaum function is used to deal with the unknown sign of uncertain control coefficient and the possible controller singularity problem. By means of Lyapunov function and the lemma of Nussbaum function, it is proved theoretically that the designed adaptive nonlinear control law can force the actual course of ships to converge to and keep at the desired course of ships, while guarantee the global uniform boundedness of all signals of the resulting closed-loop control system. The effectiveness of the proposed scheme is demonstrated through the simulations involving two ships.